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Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation

Author

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  • S. Aerts

    (HEC-ULg, University of Liege (ULg, N1))

  • G. Haesbroeck

    (Department of Mathematics, University of Liege (ULg, zone Polytech 1))

  • C. Ruwet

    (Haute Ecole Prov. de Liège, Service de Math.)

Abstract

In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations.

Suggested Citation

  • S. Aerts & G. Haesbroeck & C. Ruwet, 2018. "Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation," Statistical Papers, Springer, vol. 59(2), pages 545-579, June.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:2:d:10.1007_s00362-016-0777-4
    DOI: 10.1007/s00362-016-0777-4
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    References listed on IDEAS

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    1. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    2. Aerts, S. & Haesbroeck, G. & Ruwet, C., 2015. "Multivariate coefficients of variation: Comparison and influence functions," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 183-198.
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    Cited by:

    1. Ditzhaus, Marc & Smaga, Łukasz, 2022. "Permutation test for the multivariate coefficient of variation in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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